The resolution contends that Haywood is interfering with city employees and creating a burden by sending e-mails for "unreasonable requests" that require hours of additional work.
The council further alleges that Haywood's e-mails often contain untrue allegations against city employees and personnel.
In a video posted on YouTube by the website MitchellCountyGa.com, Haywood said she disagreed with the assertions made in the resolution and that she would be seeking legal action if the council passed the resolution.
"I have no intention of resigning," she said. "...I have retained an attorney other than (the city attorney) and you all will be hearing from that attorney."
Haywood went on to say in the meeting that in her professional training she's taught to document everything in writing for record-keeping purposes and that using e-mail is an easy way to protect both herself and the city from any kind of allegations that may come up from a verbal request.
Still, council members were not swayed, saying that her requests could be made in work sessions of the elected body rather than on the time of the city employees.
"We have a very professional staff here at the city, and they cannot do their jobs with the kind of disruptions and interference that has been going on for the last three years plus, and after discussion the other night when we asked the city attorney to draw this up, we felt like we had to do this to continue the business of the city. That's what this is about; continuing the business of the city," Councilman W.D. Palmer said.
Referencing another personnel situation in which the council previously had voted to censure its city manager only later to vote to rescind it, Councilwoman Vivian Smith said.
"We have some problems, but I think we're acting like children. Instead of getting together and talking...all of this email doesn't sometimes get to the basis of the problem. We're not able to verbalize among ourselves, this is what has caused the problem," Smith, who voted against the resolution, said. "But again, I go back to what is good for the goose is good for the gander and if it did not fit the goose it should not fit the gander."
Haywood, who had not yet returned efforts seeking comment Thursday, said in the meeting that she believes this is a personal attack made against her and questioned the timing of the resolution, as it comes during an election year.